Geometry of sliding lamellae dictates the constitutive properties of nacre-like hierarchical materials

The mechanical properties of nacre (mother-of-pearl), which are superior to those of its constituent materials, derive from a micro-architecture formed by the arrangement into parallel laminae of individual aragonite tiles with surface asperities, bonded by organic interlayers. A mechanical model is developed to determine how the contact profile that defines the geometry of the tile surface affects the constitutive response of hierarchical metamaterials of this type when they are strained in the lamellar plane. We consider the structured character of the deformation, consisting of elastic distortion of the tiles and the inelastic contribution from the disarrangements produced by relative sliding of the lamellar interfaces, which is formulated within the thermodynamic framework for irreversible processes in generalized materials. The resistance to sliding associated with constrained shear-induced dilatation of the tiles and the bridging of the organic interlayers are represented by a generalized cohesive-frictional law, effective at the level of averaged separation plane, providing a phenomenological approach that by-passes the difficulty in analytically solving the contact problem at asperities. The nominal stress–strain curves of the nacreous structure are shown to be highly dependent, qualitatively and quantitatively, on the geometry of the contact profiles. The model not only produces results that are in excellent agreement with experiments on nacre, but it can also describe complex stress–strain curves with pinched hysteresis loops having branches of various shapes, as well as serrated inelastic regimes. The versatility of this theoretical approach offers promise as a design tool for innovative metamaterials.